Some more thoughts (and I concur with all the posters that "Corbomite Maneuver" is one of the - if not the -
best episodes of TOS, especially once you consider it was the first produced of the regular series):
IMHO, Balok expresses rather human than alien behaviour. Since the real Balok does not look intimidating to other humanoids, Balok is obviously using deception ("appearances can be deceiving") on a regular basis.
I'd dare to say that therefore he is a little paranoid and suspects other sentient beings also to be deceptive on a regular basis, hence his character tests.
Considering that he misses company and conversation and wouldn't mind the company of an alien, suggests strongly that there are not any of his kind in our galaxy and that the First Federation and its planets actually do not exist (in our galaxy).
For all we know the Fesarius could be a scientific exploration ship from another galaxy and Balok just occasionally contacts "natives" he finds interesting and are suitable for First Contact procedures of the First Federation.
For the same reasons he probably gives Klingons and Romulans a wide berth. I don't think he has any interest on getting involved in any political conflicts in our galaxy (sort of a Prime Directive of the First Federation?) which could also explain why we never heard or saw him or other members of his species ever again.